A fresh look at midpoint singularities in the algebra of string fields

Abstract

In this paper we study the midpoint structure of the algebra of open strings from the standpoint of the operator/Moyal formalism. We construct a split string description for the continuous Moyal product of hep-th/0202087, study the breakdown of associativity in the star algebra, and identify in infinite sequence of new (anti)commutative coordinates for the star product in in the complex plane. We also explain how poles in the open string non(anti)commutativity parameter correspond to certain ``null'' operators which annihilate the vertex, implying that states proportional to such operators tend to have vanishing star product with other string fields. The existence of such poles, we argue, presents an obstruction to realizing a well-defined formulation of the theory in terms of a Moyal product. We also comment on the interesting, but singular, representation $L_0$ which has appeared prominently in the recent studies of Bars {\it et al}.

40 pages, 5 figures. Version to be submitted to JHEP. Some interesting and previouusly unpublished results are included here. These include both an interpretation of poles in the open string noncommutativity parameter as corresponding to null operators in the algebra, and an identification of an infinite sequence of new commutative and null coordinates in the complex $\kappa$ plane

References in corpus (11)

• Diagonal Representation of Open String Star and Moyal Product
• Virasoro operators in the continuous basis of string field theory
• On Continuous Moyal Product Structure in String Field Theory
• Continuous Half-String Representation of String Field Theory
• Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector
• Fermionic Ghosts in Moyal String Field Theory
• MSFT : Moyal Star Formulation of String Field Theory
• Locality, Causality, and an Initial Value Formulation for Open String Field Theory
• Analytic Study of Nonperturbative Solutions in Open String Field Theory
• Representation of small conformal algebra
• Moyal Representation of the String Field Star Product in the Presence of a B-background

Cited by in corpus (10)

• Comments on Schnabl's analytic solution for tachyon condensation in Witten's open string field theory
• Analytical Solutions of Open String Field Theory
• On the validity of the solution of string field theory
• Schnabl's L_0 Operator in the Continuous Basis
• Four Lectures on Analytic Solutions in Open String Field Theory
• Continuous Half-String Representation of String Field Theory
• Locality, Causality, and an Initial Value Formulation for Open String Field Theory
• Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods
• Descent Relations in Cubic Superstring Field Theory
• Lattice String Field Theory: The linear dilaton in one dimension